Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Textbook Question
Chapter 11, Problem 19P
A rectangular channel 10 ft wide carries 100 cfs on a horizontal bed at 1.0 ft depth. A smooth bump across the channel rises 4 in. above the channel bottom. Find the elevation of the liquid free surface above the bump.
P11.19
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Question
: A stream bed has a rectangular cross section 5 meters wide and a slope of
0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing
the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n =
0.015.
y = yn
2.5 m
a. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do
not need to solve the equation by hand. To get full credit, show your equation with only
one unknown.
b. Find the critical depth, yc.
c. The yn is found to be 1.8 m by solving the equation numerically. Identify the water
surface profile upstream of the dam. Explain your answer for full credit.
Q1. Check the dimensional homogeneity of the following common equations in the field of
Hydraulics.(Ca is constant, m hydraulic mean depth and i the longitudinal slope of the channel)
(1) Q = Ca a√2gH and
(ii) v = C√mi
Water flows over a spillway of a dam. At the bottom of the spillway, water flows into a rectangular
concrete-finished channel (width - 50 ft) with a slope of 0.005. Let n-0.0206.
2.5 ft
d, - 2.9 ft
a) Calculate the velocity in the channel at the section where the depth is 2.9 ft. Use Manning's
equation. (15)
b) Determine Froude number at the section where the depth is 2.9 ft and classify the flow. (15)
c) Classify the flow where the depth is 2.5 ft and prove your classification. (15)
d) What do you expect the flow to be at depth d2 (just an educated guess)? (5)
Chapter 11 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 11 - Verify the equation given in Table 11.1 for the...Ch. 11 - A pebble is dropped into a stream of water that...Ch. 11 - Solution of the complete differential equations...Ch. 11 - A water flow rate of 250 cfs flows at a depth of 5...Ch. 11 - Determine and plot the relation between water...Ch. 11 - Capillary waves (ripples) are small amplitude and...Ch. 11 - The Froude number characterizes flow with a free...Ch. 11 - Consider waves on the surface of a tank of water...Ch. 11 - A submerged body traveling horizontally beneath a...Ch. 11 - Water flows in a rectangular channel at a depth of...
Ch. 11 - A partially open sluice gate in a 5-m-wide...Ch. 11 - Find the critical depth for flow at 3 m3/s in a...Ch. 11 - Flow occurs in a rectangular channel of 6 m width...Ch. 11 - What is the maximum flow rate that may occur in a...Ch. 11 - A rectangular channel carries a discharge of 10...Ch. 11 - Flow in the channel of Problem 11.15 has a...Ch. 11 - Consider the Venturi flume shown. The bed is...Ch. 11 - Eleven cubic meters per second of water are...Ch. 11 - A rectangular channel 10 ft wide carries 100 cfs...Ch. 11 - At what depths can 800 cfs flow in a trapezoidal...Ch. 11 - At a section of a 10-ft-wide rectangular channel,...Ch. 11 - Water, at 3 ft/s and 2 ft depth, approaches a...Ch. 11 - A horizontal rectangular channel 3 ft wide...Ch. 11 - A hydraulic jump occurs in a rectangular channel...Ch. 11 - A hydraulic jump occurs in a wide horizontal...Ch. 11 - A hydraulic jump occurs in a rectangular channel....Ch. 11 - The depths of water upstream and downstream from a...Ch. 11 - Calculate y2, h, and y3 for this two-dimensional...Ch. 11 - The hydraulic jump may be used as a crude flow...Ch. 11 - A hydraulic jump occurs on a horizontal apron...Ch. 11 - A hydraulic jump occurs in a rectangular channel....Ch. 11 - A positive surge wave, or moving hydraulic jump,...Ch. 11 - A 2-m-wide rectangular channel with a bed slope of...Ch. 11 - Determine the uniform flow depth in a rectangular...Ch. 11 - Determine the uniform flow depth in a trapezoidal...Ch. 11 - Water flows uniformly at a depth of 1.2 m in a...Ch. 11 - This large uniform open channel flow is to be...Ch. 11 - A rectangular flume built of timber is 3 ft wide....Ch. 11 - A channel with square cross section is to carry 20...Ch. 11 - A triangular channel with side angles of 45 is to...Ch. 11 - A flume of timber has as its cross section an...Ch. 11 - At what depth will 4.25 m3/s flow uniformly in a...Ch. 11 - A semicircular trough of corrugated steel, with...Ch. 11 - A rectangular flume built of concrete with 1 ft...Ch. 11 - Water flows in a trapezoidal channel at a flow...Ch. 11 - What slope is necessary to carry 11 m3/s uniformly...Ch. 11 - Find the normal depth for the channel of Problem...Ch. 11 - For a trapezoidal shaped channel with n = 0.014...Ch. 11 - Compute the critical depth for the channel in...Ch. 11 - A trapezoidal canal lined with brick has side...Ch. 11 - An optimum rectangular storm sewer channel made of...Ch. 11 - For a sharp-crested suppressed weir of length B =...Ch. 11 - A rectangular sharp-crested weir with end...Ch. 11 - What is the depth of water behind a rectangular...Ch. 11 - A broad-crested weir 0.9 m high has a flat crest...Ch. 11 - The head on a 90 V-notch weir is 1.5 ft. Determine...
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